Which of the following sentences best characterizes the relationship among Type

Question

Which of the following sentences best characterizes the relationship among Type I error, Type II error, sample size, and the power of hypotheses testing? a) Type I error is inflated as Type II error decreases, neither is related to sample size. b) Hypothesis testing does not rely on sample size, Type I or II error. c) When sample size is small, there is a higher chance of committing Type II error and decreased power to reject the null hypothesis d) When sample size is small there is a higher chance of committing Type I error and increased power to reject the null hypothesis.

Explanation / Answer

Solution-

First we will define the basic terms-

Type 1 error - probability of rejecting null hypothesis when it is true.

Type 2 error - probability of not rejecting null hypothesis when it is false.

Power - probability of rejecting null hypothesis when it is false.

When sample size is small, then test statistic is large and the probability of rejecting the null hypothesis increases. So probability of committing type 1 error increases. As type 1 error increases, then power must also increase.

hence option D is best.

Thanks!

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